Why does poissons ratio affect press fit force? 2

[necktwist]

The press fit force is a pretty cool equation that also incorporates poissons ratio. Here is a link to it.

My main question is why does increasing poissons ratio in the boss (outer ring of the pressfit, Eo above) reduce axial slip pressure, but when you increase poissons ratio of the shaft (Ei above) it actually increases axial slip pressure?

i can't visualize this mechanism, i can kinda grasp why increased poissons ratio of the boss or outer ring would cause a necking type reduction of cross section if its under hoop stress (however the part of the equation that uses poissons ratio does not calcualte hoop stress it only deals with diametrical interference),but why on earth will increasing poissons ratio increase the press fit pressure?

Thanks very much, Jeff

 

[electricpete]

I would think:

For the outer cylinder, the tangential tension stress creates a radial contraction that tends to neck down the outer cylinder and reduce the fit pressure.

For the inner cylinder, the tangential compression stress creates a radial expansion that tends to expand the inner cylinder and increase fit pressure.


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(2B)+(2B)' ?

 

[Wrenchbender]

What Pete said. (For elastic & axisymmetric.) Also sometimes its helpful to look thru the derivation of equations just to follow the path of the variable of interest. The end result is often not intuitively obvious, but its still good to question things.

 

[necktwist]

electricpete.. thanks for that response. i agree with you and also think there is the issue of 'uncompressible' material that happens as the poissons ratio approaches 0.5, hence you can't squeeze it any more in a closed system.

Bestwrench, i am about to go through that derivation, however can either of you common on the direction of radial contraction that occurres on the outer cylinder? you would think it would contract but that the axis would be centered around the surface of the inner rod, but that may or may not limit the necking down, just a thought. thanks much!!

 

[IDS]

I'm not familiar with these calculations, but assuming the outer cylinder has a uniform longitudinal pressure applied to the ends the Poisson's Ratio effect would cause both the inner and outer surface to expand outwards, so why would you expect a contraction?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[necktwist]

IDS, the outer boss is not constrained at the ends, its free to move. Also, the outer is in tension so we are saying it would either neck or not neck.

Also, whats interesting in this formula is how little effect poissson's ratio has. its only added or subtracted in the formula to a much larger number (at least on the outer ring formula, on the inner its subtracted from 1).

What are your thoughts on that?

 

[Compositepro]

Imagine your parts were made from rubber. Trying to press a rubber plug into a hole is difficult because the plug expands due to the axial pressure. If you try to get a piece of rubber hose onto a steel nipple the hose diameter will expand if you press it on. The hole diameter will shrink if you you try to pull the hose onto the nipple. These are Poisson effects. Rubber simply has a high Poisson ratio and high strain so the effect can more easily be observed.

A point you may be unclear about is that the press fit forces create axial compression in the parts even though it is a shear force at the points of contact.

 

[Canadieng]

Slightly offtopic, but interesting trivia nonetheless:

Expanding on Compositepro's observations:

One of the big reasons why cork is so useful in making stoppers for wine bottles is that it has, essentially, a Poisson's ratio of zero. That is, when the cork gets squeezed into the bottle, there is no bulge that forms outside the glass that needs to be overcome.